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A010693
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Periodic sequence: Repeat 2,3.
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21
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2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3
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OFFSET
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0,1
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COMMENTS
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a(n) = smallest prime divisor of n!! for n >= 2. For biggest prime divisor of n!! see A139421. - Artur Jasinski, Apr 21 2008
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-3, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=-charpoly(A,-2). - Milan Janjic, Jan 27 2010
Simple continued fraction of 1+sqrt(5/3) = A176020. - R. J. Mathar, Mar 08 2012
p(n) = a(n-1) is the Abelian complexity function of the Thue-Morse word A010060. - Nathan Fox, Mar 12 2013
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LINKS
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Table of n, a(n) for n=0..101.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 466
G. Richomme, K. Saari, L. Q. Zamboni, Abelian complexity in minimal subshifts, J. London Math. Soc. 83(1) (2011) 79-95.
G. Richomme, K. Saari, L. Q. Zamboni, Abelian complexity in minimal subshifts, arXiv:0911.2914 [math.CO], 2009.
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FORMULA
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a(n) = 5/2 - ((-1)^n)/2.
a(n) = 2 + (n mod 2) = A007395(n) + A000035(n). - Reinhard Zumkeller, Mar 23 2005
a(n) = A020639(A016767(n)) for n>0. - Reinhard Zumkeller, Jan 29 2009
From Jaume Oliver Lafont, Mar 20 2009: (Start)
G.f.:(2+3*x)/(1-x^2).
Linear recurrence: a(0)=2, a(1)=3, a(n)=a(n-2) for n>=2. (End)
a(n) = A001615(2n)/A001615(n) for n > 0. - Enrique Pérez Herrero, Jun 06 2012
a(n) = floor((n+1)*5/2) - floor((n)*5/2). - Hailey R. Olafson, Jul 23 2014
a(n) = 3 - ((n+1) mod 2). - Wesley Ivan Hurt, Jul 24 2014
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MAPLE
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A010693:=n->2+(n mod 2): seq(A010693(n), n=0..100); # Wesley Ivan Hurt, Jul 24 2014
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MATHEMATICA
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Table[5/2 - (-1)^n/2, {n, 0, 100}] or a = {}; Do[b = First[First[FactorInteger[n!! ]]]; AppendTo[a, b], {n, 2, 1000}]; a (* Artur Jasinski, Apr 21 2008 *)
2 + Mod[Range[0, 100], 2] (* Wesley Ivan Hurt, Jul 24 2014 *)
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PROG
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(Haskell)
a010693 = (+ 2) . (`mod` 2) -- Reinhard Zumkeller, Nov 27 2012
a010693_list = cycle [2, 3] -- Reinhard Zumkeller, Mar 29 2012
(MAGMA) [2 + (n mod 2) : n in [0..100]]; // Wesley Ivan Hurt, Jul 24 2014
(PARI) a(n)=3 - (n+1)%2 \\ Charles R Greathouse IV, May 09 2016
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CROSSREFS
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Cf. A139421.
Cf. A026549 (partial products).
Sequence in context: A274821 A275720 A165587 * A158478 A139713 A171465
Adjacent sequences: A010690 A010691 A010692 * A010694 A010695 A010696
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Definition rewritten by Bruno Berselli, Sep 30 2011
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STATUS
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approved
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